Time Variation Of Field Research Articles

Spatial distribution characteristics and mechanism of nonhydrological time-variable gravity in mainland China

The purpose of this study is to explore nonhydrological mass transfer in China continent. For this purpose, gravity recovery and climate experiment (GRACE) data were obtained to study the spatial distribution of time variant gravity signals in China continent. Then, from auxiliary hydrological data processed according to the current hydrological model, a new more comprehensive hydrological model of China continent was constructed. Finally, the time variant signals of this new hydrological model were removed from the time variant gravity field computed from GRACE data, thus obtaining a description of the nonhydrological mass transfer of China continent. The physical sources and mechanisms of the resulting mass transfer are then discussed. The improved, more realistic, hydrological model used here was created by selecting the hydrological components with the best correlations in existing hydrological models, by use of correlation calculation, analysis, and comparison. This improved model includes water in soils and deeper strata, in the vegetation canopy, in lakes, snow, and glaciers, and in other water components (mainly reservoir storage, swamps, and rivers). The spatial distribution of the transfer signals due to nonhydrological mass in China continent was obtained by subtracting the combined hydrological model from the GRACE time-variable gravity field. The results show that the nonhydrological signals in China continent collected in GRACE data were mainly positive signals, and were distributed in the Bohai Rim and the northern and eastern parts of the Tibetan Plateau. The above nonhydrological mass transfer signals have been studied further and are discussed. The results show that the nonhydrological mass migration signals in the Bohai Rim region originate primarily from sea level change and marine sediment accumulation. The mass accumulation from Indian plate collision in the Tibetan Plateau appears to be the main reason for the increase in the residual gravity field in that region.

An Adaptive Regularized Solution to Inverse Ill-Posed Models

The ill-posed models are widely encountered in various inversions of geodesy and remote sensing. The regularization approaches can significantly stabilize the solution to ill-posed models since the high-frequency noise is effectively suppressed. Although the famous Tikhonov regularization and truncated singular value decomposition (TSVD) regularization have been widely applied in various geodetic applications, there still remain theoretical drawbacks for either single regularization. For Tikhonov regularization, given a regularization parameter, the low-frequency terms are over regularized, and high-frequency terms are under regularized. For TSVD regularization, some medium-frequency terms will be mistaken for high-frequency terms to be truncated and the hidden signals will be lost. For this reason, we propose an adaptive regularized solution in spectral form, which adaptively divides the terms of different frequencies into three kinds: (i) the low-frequency terms are not regularized; (ii) the medium-frequency terms are regularized by the Tikhonov method; (iii) the high-frequency terms are regularized by TSVD method. The analytical conditions for determining the term sets are derived based on the criteria that the introduced biases should be smaller than the reduced errors, in other words, the mean squared error (MSE) should be reduced. The two examples are presented to demonstrate the performance of our adaptive regularization. The first numerical example is solving the Fredholm integral equation of the first kind, which is widely encountered in remote sensing inversions. The simulations clearly demonstrate that the adaptive regularized solution can improve the MSE of ordinary Tikhonov and TSVD regularized functions by 25.00% and 9.09%, respectively; In the second example, we apply the new method to investigate the mass variation of the Yangtze River Basin based on the Gravity Recovery and Climate Experiment (GRACE) time-variable gravity field model. The Tongji-Grace 2018 monthly gravity field solutions from April 2002 to December 2016 are used to construct the mascon observation equation. The results show that our method also outperforms the ordinary Tikhonov and TSVD regularized solutions, with mean MSE reductions of about 13.40% and 11.69%, respectively. Furthermore, the spatial resolution of secular trend derived by our method are improved and the signal-to-noise ratio (SNR) of mass variation series is higher than the other two regularizations.

Analysis of the Influencing Factors of Drought Events Based on GRACE Data under Different Climatic Conditions: A Case Study in Mainland China

The occurrence of droughts has become more frequent, and their intensity has increased in mainland China. With the aim of better understanding the influence of climate background on drought events in this region, we analyzed the role of the drought-related factors and extreme climate in the formation of droughts by investigating the relationship between the drought severity index (denoted as GRACE-DSI) based on the terrestrial water storage changes (TWSCs) derived from Gravity Recovery and Climate Experiment (GRACE) time-variable gravity fields and drought-related factors/extreme climate. The results show that GRACE-DSI was consistent with the self-calibrating Palmer Drought Severity Index in mainland China, especially for the subtropical monsoon climate, with a correlation of 0.72. Precipitation (PPT) and evapotranspiration (ET) are the main factors causing drought events. However, they play different roles under different climate settings. The regions under temperate monsoon climate and subtropical monsoon climate were more impacted by PPT, while ET played a leading role in the regions under temperate continental climate and plateau mountain climate. Moreover, El Niño–Southern Oscillation (ENSO) and North Atlantic Oscillation (NAO) events mainly caused abnormalities in PPT and ET by affecting the strength of monsoons (East Asian and Indian monsoon) and regional highs (Subtropical High, Siberian High, Central Asian High, etc.). As a result, the various affected regions were prone to droughts during ENSO or NAO events, which disturbed the normal operation of atmospheric circulation in different ways. The results of this study are valuable in the efforts to understand the formation mechanism of drought events in mainland China.

Time-Variable Gravity Field from the Combination of HLSST and SLR

The Earth’s time-variable gravity field is of great significance to study mass change within the Earth’s system. Since 2002, the NASA-DLR Gravity Recovery and Climate Experiment (GRACE) and its successor GRACE follow-on mission provide observations of monthly changes in the Earth gravity field with unprecedented accuracy and resolution by employing low-low satellite-to-satellite tracking (LLSST) measurements. In addition to LLSST, monthly gravity field models can be acquired from satellite laser ranging (SLR) and high-low satellite-to-satellite tracking (HLSST). The monthly gravity field solutions HLSST+SLR were derived by combining HLSST observations of low earth orbiting (LEO) satellites with SLR observations of geodetic satellites. Bandpass filtering was applied to the harmonic coefficients of HLSST+SLR solutions to reduce noise. In this study, we analyzed the performance of the monthly HLSST+SLR solutions in the spectral and spatial domains. The results show that: (1) the accuracies of HLSST+SLR solutions are comparable to those from GRACE for coefficients below degree 10, and significantly improved compared to those of SLR-only and HLSST-only solutions; (2) the effective spatial resolution could reach 1000 km, corresponding to the spherical harmonic coefficient degree 20, which is higher than that of the HLSST-only solutions. Compared with the GRACE solutions, the global mass redistribution features and magnitudes can be well identified from HLSST+SLR solutions at the spatial resolution of 1000 km, although with much noise. In the applications of regional mass recovery, the seasonal variations over the Amazon Basin and the long-term trend over Greenland derived from HLSST+SLR solutions truncated to degree 20 agree well with those from GRACE solutions without truncation, and the RMS of mass variations is 282 Gt over the Amazon Basin and 192 Gt in Greenland. We conclude that HLSST+SLR can be an alternative option to estimate temporal changes in the Earth gravity field, although with far less spatial resolution and lower accuracy than that offered by GRACE. This approach can monitor the large-scale mass transport during the data gaps between the GRACE and the GRACE follow-on missions.

Evaluation of GRACE/GRACE Follow-On Time-Variable Gravity Field Models for Earthquake Detection above Mw8.0s in Spectral Domain

This study compares the Gravity Recovery And Climate Experiment (GRACE)/GRACE Follow-On (GFO) errors with the coseismic gravity variations generated by earthquakes above Mw8.0s that occurred during April 2002~June 2017 and evaluates the influence of monthly model errors on the coseismic signal detection. The results show that the precision of GFO monthly models is approximately 38% higher than that of the GRACE monthly model and all the detected earthquakes have signal-to-noise ratio (SNR) larger than 1.8. The study concludes that the precision of the time-variable gravity fields should be improved by at least one order in order to detect all the coseismic gravity signals of earthquakes with M ≥ 8.0. By comparing the spectral intensity distribution of the GFO stack errors and the 2019 Mw8.0 Peru earthquake, it is found that the precision of the current GFO monthly model meets the requirement to detect the coseismic signal of the earthquake. However, due to the limited time length of the observations and the interference of the hydrological signal, the coseismic signals are, in practice, difficult to extract currently.

Using Swarm to Detect Total Water Storage Changes in 26 Global Basins (Taking the Amazon Basin, Volga Basin and Zambezi Basin as Examples)

The Gravity Recovery and Climate Experiment (GRACE) satellite provides time-varying gravity field models that can detect total water storage change (TWSC) from April 2002 to June 2017, and its second-generation satellite, GRACE Follow-On (GRACE-FO), provides models from June 2018, so there is a one year gap. Swarm satellites are equipped with Global Positioning System (GPS) receivers, which can be used to recover the Earth’s time-varying gravitational field. Swarm’s time-varying gravitational field models (from December 2013 to June 2018) were solved by the International Combination Service for Time-variable Gravity Field Solutions (COST-G) and the Astronomical Institute of the Czech Academy of Sciences (ASI). On a timely scale, Swarm has the potential to fill the gap between the two generations of GRACE satellites. In this paper, using 26 global watersheds as the study area, first, we explored the optimal data processing strategy for Swarm and then obtained the Swarm-TWSC of each watershed based on the optimal results. Second, we evaluated Swarm’s accuracy in detecting regional water storage variations, analyzed the reasons for its superior and inferior performance in different regions, and systematically explored its potential in detecting terrestrial water storage changes in land areas. Finally, we constructed the time series of terrestrial water storage changes from 2002 to 2019 by combining GRACE, Swarm, and GRACE-FO for the Amazon, Volga, and Zambezi Basins. The results show that the optimal data processing strategy of Swarm is different from that of GRACE. The optimal results of Swarm-TWSC were explored in 26 watersheds worldwide; its accuracy is related to the area size, runoff volume, total annual mass change, and instantaneous mass change of the watershed itself, among which the latter is the main factor affecting Swarm-TWSC. Knowledge of the Swarm-TWSC of 26 basins constructed in this paper is important to study long-term water storage changes in basins.

Determination of the degree 120 time-variable gravity field in the Sichuan-Yunnan region using Slepian functions and terrestrial measurements

The terrestrial time-variable gravity measurements are characterized by a high signal-to-noise ratio and sensitivity to the sources of mass change in the Earth’s crust. These gravity data have many applications, such as surface deformation, groundwater storage changes, and mass migration before and after earthquakes. Based on repeated terrestrial gravity measurements at 198 gravity stations in the Sichuan-Yunnan region (SYR) from 2015 to 2017, we determine a time series of degree 120 gravity fields using the localized spherical harmonic (Slepian) basis functions. Our results show that adopting the first 6 Slepian basis functions is sufficient for effective localized Slepian modeling in the SYR. The differences between two gravity campaigns at the same time of year show an obvious correlation with tectonic features. The degree 120 time-variable gravity models presented in this paper will benefit the study of the regional mass migration inside the crust of the SYR and supplement the existing geophysical models for the China Seismic Experimental Site.

Gravity Field Recovery and Error Analysis for the MOCASS Mission Proposal Based on Cold Atom Interferometry

Satellite missions providing data for a continuous monitoring of the Earth gravity field and its changes are fundamental to study climate changes, hydrology, sea level changes, and solid Earth phenomena. GRACE-FO (Gravity Recovery and Climate Experiment Follow-On) mission was launched in 2018 and NGGM (Next Generation Gravity Mission) studies are ongoing for the long-term monitoring of the time-variable gravity field. In recent years, an innovative mission concept for gravity measurements has also emerged, exploiting a spaceborne gravity gradio-meter based on cold atom interferometers. In particular, a team of researchers from Italian universities and research institutions has proposed a mission concept called MOCASS (Mass Observation with Cold Atom Sensors in Space) and conducted the study to investigate the performance of a cold atom gradiometer on board a low Earth orbiter and its impact on the modeling of different geophysical phenomena. This paper presents the analysis of the gravity gradient data attainable by such a mission. Firstly, the mathematical model for the MOCASS data processing will be described. Then numerical simulations will be presented, considering different satellite orbital altitudes, pointing modes and instrument configurations (single-arm and double-arm); overall, data were simulated for twenty different observation scenarios. Finally, the simulation results will be illustrated, showing the applicability of the proposed concept and the improvement in modeling the static gravity field with respect to GOCE (Gravity Field and Steady-State Ocean Circulation Explorer).

Earth’s Time-Variable Gravity from GRACE Follow-On K-Band Range-Rates and Pseudo-Observed Orbits

During its science phase from 2002–2017, the low-low satellite-to-satellite tracking mission Gravity Field Recovery And Climate Experiment (GRACE) provided an insight into Earth’s time-variable gravity (TVG). The unprecedented quality of gravity field solutions from GRACE sensor data improved the understanding of mass changes in Earth’s system considerably. Monthly gravity field solutions as the main products of the GRACE mission, published by several analysis centers (ACs) from Europe, USA and China, became indispensable products for quantifying terrestrial water storage, ice sheet mass balance and sea level change. The successor mission GRACE Follow-On (GRACE-FO) was launched in May 2018 and proceeds observing Earth’s TVG. The Institute of Geodesy (IfE) at Leibniz University Hannover (LUH) is one of the most recent ACs. The purpose of this article is to give a detailed insight into the gravity field recovery processing strategy applied at LUH; to compare the obtained gravity field results to the gravity field solutions of other established ACs; and to compare the GRACE-FO performance to that of the preceding GRACE mission in terms of post-fit residuals. We use the in-house-developed MATLAB-based GRACE-SIGMA software to compute unconstrained solutions based on the generalized orbit determination of 3 h arcs. K-band range-rates (KBRR) and kinematic orbits are used as (pseudo)-observations. A comparison of the obtained solutions to the results of the GRACE-FO Science Data System (SDS) and Combination Service for Time-variable Gravity Fields (COST-G) ACs, reveals a competitive quality of our solutions. While the spectral and spatial noise levels slightly differ, the signal content of the solutions is similar among all ACs. The carried out comparison of GRACE and GRACE-FO KBRR post-fit residuals highlights an improvement of the GRACE-FO K-band ranging system performance. The overall amplitude of GRACE-FO post-fit residuals is about three times smaller, compared to GRACE. GRACE-FO post-fit residuals show less systematics, compared to GRACE. Nevertheless, the power spectral density of GRACE-FO and GRACE post-fit residuals is dominated by similar spikes located at multiples of the orbital and daily frequencies. To our knowledge, the detailed origin of these spikes and their influence on the gravity field recovery quality were not addressed in any study so far and therefore deserve further attention in the future. Presented results are based on 29 monthly gravity field solutions from June 2018 until December 2020. The regularly updated LUH-GRACE-FO-2020 time series of monthly gravity field solutions can be found on the website of the International Centre for Global Earth Models (ICGEM) and in LUH’s research data repository. These operationally published products complement the time series of the already established ACs and allow for a continuous and independent assessment of mass changes in Earth’s system.

Influence of the Low-Frequency Error of the Residual Orbit on Recovering Time-Variable Gravity Field from the Satellite-To-Satellite Tracking Mission

When using the dynamic approach to recover the time-variable gravity field, the reference orbit generated by the perturbation model and the non-conservative force observed from the accelerometer should be introduced at first, and then the observation equations of the residual orbit and the residual range rate are established. This introduces a perturbation model error and instrument noise. Thus, there are low-frequency errors in the residual orbit and the residual range rate. Currently, most studies only focus on the low-frequency error of the residual range rate, neglecting the influence of the low-frequency error in the residual orbit. Therefore, under the condition of the perturbation model error and instrument noise including the constant term and 1CPR term, the low-frequency error formulas of the residual orbit and residual range rate are derived according to the characteristics of the solution of the Hill equation. Then, the influence of the low-frequency error on the residuals is analyzed by using the simulation and the real data processing respectively. In the simulation and real data processing, the accuracy of the recovered gravity field can maintain a good consistency for different arc lengths by removing the low-frequency error in the residual orbit. Finally, the time-variable gravity field model UCAS-IGG (University of Chinese Academy of Sciences-Institute of Geodesy and Geophysics) was solved from January 2005 to February 2010 by removing the low-frequency error of the residual orbit and residual range rate. Compared with the official institutions, the UCAS-IGG presents a good consistency in the estimating time-variable gravity field signal. This study demonstrates how the effect of the low-frequency error of the residual orbit should be taken into consideration when the longer arc length is used to recover a time-variable gravity field. Using a long arc length can reduce the variables of the initial state and recover the influence of the small force.

Bridging the gap between GRACE and GRACE follow-on monthly gravity field solutions using improved multichannel singular spectrum analysis

The gap between the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-on mission (GRACE-FO) is a crucial problem, leading to discontinuous global mass change information from time-variable gravity field solutions. We aim to use the improved Multichannel Singular Spectrum Analysis (MSSA) to fill the gap and reconstruct the continual global mass change signals in this study. The one-year gravity field gap is filled with improved MSSA based on the Release 06 (RL06) monthly gravity field models provided by Center for Space Research (CSR) truncated to d/o 60 and further compared with Swarm monthly solutions (d/o 40). The results show that the infilled gravity field models agree with the Swarm solutions, indicating that improved MSSA can reliably bridge the gap between GRACE and GRACE-FO missions. Moreover, relative to the Global Land Data Assimilation System (GLDAS) Noah model, the infilled gravity field models have higher correlation coefficients and smaller root mean squared errors than Swarm solutions for the mass change signals over Congo, Lena and Fraser river basins. According to the simulation results using the same gap as GRACE and GRACE-FO, improved MSSA can fill the gap very efficiently and reliably in 25 major river basins over the World.

Analysis of limitations on recovery of gravity field based on satellite gravity gradient data

Although satellite gravity gradient data plays a great role in determining short-wavelength part of static gravity field model, accuracy of the long-wavelength part of gravity field model recovered by them are poor, which leads to only a few applications in time-variable gravity investigation. The reason is that some factors limit the accuracy of the gravity field recovered using gradient data, including accuracy of the gravity gradient observations, measurement bandwidth (MBW) of gradiometer, satellite inclination, etc. This paper aims at analyzing the influence of these limitations on gravity field recovery and discusses the possibility of time-variable gravity field detection by using gravity gradient observations. Firstly, for arbitrary satellite orbit inclination, we give the frequency distributions of all the components of gravity gradients (i.e. Txx,Tyy,Tzz,Txy,TxzandTyz, ). The results show that the maximum frequency of each component of the gravity gradients is the same, i.e. l/Ts (l is degree of the gravity field model, Ts is the orbital periods), and it is not influenced by the inclination of the satellite orbits. Secondly, the paper gives a theory proof to explain why only the low orders of the coefficients are influenced by polar gaps. Big polar gaps are experimented by a numerical test with inclination of 45°. Finally, considering that the measurement bandwidth can be expanded and accuracy of gradient observations can be improved by superconducting gravity gradiometer (SGG) compared to gradiometer used in Gravity field and steady-state Ocean Circulation Explorer (GOCE), the possibility of detecting time-variable gravity using gravity gradient observations is discussed. The results show that the SGG creates errors in MBW with magnitude of 0.014 mE, which is smaller than the magnitude of the time-variable gravity gradient signals (i.e., 0.02 mE) derived from Gravity Recovery and Climate Experiment (GRACE) gravity field models. This indicates the potential of SGG in time-variable gravity detection.

A hybrid approach for recovering high-resolution temporal gravity fields from satellite laser ranging

A new approach to recover time-variable gravity fields from satellite laser ranging (SLR) is presented. It takes up the concept of lumped coefficients by representing the temporal changes of the Earth’s gravity field by spatial patterns via combinations of spherical harmonics. These patterns are derived from the GRACE mission by decomposing the series of monthly gravity field solutions into empirical orthogonal functions (EOFs). The basic idea of the approach is then to use the leading EOFs as base functions in the gravity field modelling and to adjust the respective scaling factors straightforward within the dynamic orbit computation; only for the lowest degrees, the spherical harmonic coefficients are estimated separately. As a result, the estimated gravity fields have formally the same spatial resolution as GRACE. It is shown that, within the GRACE time frame, both the secular and the seasonal signals in the GRACE time series are reproduced with high accuracy. In the period prior to GRACE, the SLR solutions are in good agreement with other techniques and models and confirm, for instance, that the Greenland ice sheet was stable until the late 1990s. Further validation is done with the first monthly fields from GRACE Follow-On, showing a similar agreement as with GRACE itself. Significant differences to the reference data only emerge occasionally when zooming into smaller river basins with strong interannual mass variations. In such cases, the approach reaches its limits which are set by the low spectral sensitivity of the SLR satellites and the strong constraints exerted by the EOFs. The benefit achieved by the enhanced spatial resolution has to be seen, therefore, primarily in the proper capturing of the mass signal in medium or large areas rather than in the opportunity to focus on isolated spatial details.

Benchmark data for verifying background model implementations in orbit and gravity field determination software

Abstract. In the framework of the COmbination Service for Time-variable Gravity fields (COST-G) gravity field solutions from different analysis centres are combined to provide a consolidated solution of improved quality and robustness to the user. As in many other satellite-related sciences, the correct application of background models plays a crucial role in gravity field determination. Therefore, we publish a set of data of various commonly used forces in orbit and gravity field modelling (Earth's gravity field, tides etc.) evaluated along a one day orbit arc of GRACE, together with auxiliary data to enable easy comparisons. The benchmark data is compiled with the GROOPS software by the Institute of Geodesy (IfG) at Graz University of Technology. It is intended to be used as a reference data set and provides the opportunity to test the implementation of these models at various institutions involved in orbit and gravity field determination from satellite tracking data. In view of the COST-G GRACE and GRACE Follow-On gravity field combinations, we document the outcome of the comparison of the background force models for the Bernese GNSS software from AIUB (Astronomical Institute, University of Bern), the EPOS software of the German Research Centre for Geosciences (GFZ), the GINS software, developed and maintained by the Groupe de Recherche de Géodésie Spatiale (GRGS), the GRACE-SIGMA software of the Leibniz University of Hannover (LUH) and the GRASP software also developed at LUH. We consider differences in the force modelling for GRACE (-FO) which are one order of magnitude smaller than the accelerometer noise of about 10−10 m s−2 to be negligible and formulate this as a benchmark for new analysis centres, which are interested to contribute to the COST-G initiative.

Comparison of Terrestrial Water Storage Changes Derived from GRACE/GRACE-FO and Swarm: A Case Study in the Amazon River Basin

The mass changes in the Earth’s surface internally derived from the Gravity Recovery and Climate Experiment (GRACE) and the GRACE Follow-On (GRACE-FO) missions have played an important role in the research of various geophysical phenomena. However, the one-year data gap between these two missions has broken the continuity of this geophysical research. In order to assess the feasibility of using the Swarm time-variable gravity field (TVGF) to bridge the data gap, we compared Swarm with the GRACE/GRACE-FO models in terms of model accuracy, observation noise and inverted terrestrial water storage change (TWSC). The results of the comparison showed that the difference between the degree-error root mean square (RMS) of the two models is small, within degree 10. The correlation between the spherical harmonic coefficients of the two models is also relatively high, below degree 17. The observation noise values of GRACE/GRACE-FO are smaller than those of Swarm. Therefore, the latter model requires a larger filter radius to lower these noise levels. According to the correlation coefficients and the time series map of TWSC in the Amazon River basin, the results of GRACE and Swarm are similar. In addition, the TWSC signals were further analyzed. The long-term trend changes of TWSC derived from GRACE/GRACE-FO and the International Combination Service for Time-variable Gravity Fields (COST-G)-Swarm over the period from December 2013 to May 2020 were −0.72 and −1.05 cm/year, respectively. The annual amplitudes of two models are 15.65 and 15.39 cm, respectively. The corresponding annual phases are −1.36 and −1.33 rad, respectively. Our results verified that the Swarm TVGF has the potential to extract TWSC signals in the Amazon River basin and can serve as a complement to GRACE/GRACE-FO data for detecting TWSC in local areas.

Routes of the Upper Branch of the Atlantic Meridional Overturning Circulation according to an Ocean State Estimate.

The origins of the upper branch of the Atlantic meridional overturning circulation (AMOC) are traced with backward‐in‐time Lagrangian trajectories, quantifying the partition of volume transport between different routes of entry from the Indo‐Pacific into the Atlantic. Particles are advected by the velocity field from a recent release of “Estimating the Circulation and Climate of the Ocean” (ECCOv4). This global time‐variable velocity field is a dynamically consistent interpolation of over 1 billion oceanographic observations collected between 1992 and 2015. Of the 13.6 Sverdrups (1 Sv = m/s) flowing northward across 6°S, 15% enters the Atlantic from Drake Passage, 35% enters from the straits between Asia and Australia (Indonesian Throughflow), and 49% comes from the region south of Australia (Tasman Leakage). Because of blending in the Agulhas region, water mass properties in the South Atlantic are not a good indicator of origin.

Additional methods for the stable calculation of isotropic Gaussian filter coefficients: The case of a truncated filter kernel

The isotropic Gaussian filter is frequently used as a post-processing method for mitigating errors in Gravity Recovery and Climate Experiment (GRACE) time-variable gravity field solutions. It is known that the recurrent calculation of isotropic Gaussian filter coefficients in the spherical harmonic domain results in numerical instabilities. This issue has been recently resolved by Piretzidis & Sideris (Computers & Geosciences 133:104303) for the case of a global Gaussian filter. In this paper, we extend this work for the case of a regional Gaussian filter (i.e., a Gaussian filter with a truncated kernel). We show that instabilities also occur when the coefficients of a regional Gaussian filter are calculated using a conventional recurrence relation, and we provide methods for their proper treatment. We also briefly present some theoretical preliminaries related to recurrence relations and examine algorithms (i.e., initial value and boundary value algorithms) for their stable evaluation. Our analysis indicates that the initial value algorithms are ineffective for the calculation of regional Gaussian filter coefficients, contrary to the global Gaussian filter. The comparison of the boundary value algorithms shows that the Thomas and lower-upper (LU) decomposition algorithms are the most suitable for this case. Their main advantage is their insusceptibility to numerical limitations, such as overflow errors. The Thomas algorithm is also the most efficient in terms of computational speed.

GRACE-FO precise orbit determination and gravity recovery

The gravity recovery and climate experiment follow-on (GRACE-FO) satellites, launched in May of 2018, are equipped with geodetic quality GPS receivers for precise orbit determination (POD) and gravity recovery. The primary objective of the GRACE-FO mission is to map the time-variable and mean gravity field of the Earth. To achieve this goal, both GRACE-FO satellites are additionally equipped with a K-band ranging (KBR) system, accelerometers and star trackers. Data processing strategies, data weighting approaches and impacts of observation types and rates are investigated in order to determine the most efficient approach for processing GRACE-FO multi-type data for precise orbit determination and gravity recovery. Two GPS observation types, un-differenced (UD) and double-differenced (DD) observations in general can be used for GPS-based POD and gravity recovery. The GRACE-FO KBR observations are mainly used for gravity recovery, but they can be also used for POD to improve the relative orbit accuracy. The main purpose of this paper is to study the impacts of the DD, UD and KBR observations on GRACE-FO POD and gravity recovery. The precise orbit accuracy is assessed using several tests, which include analysis of orbital fits, satellite laser ranging residuals, KBR range residuals and orbit comparisons. The gravity recovery is validated by comparing different gravity solutions through coefficient-wise comparison, degree difference variances and water height variations over the whole Earth and selected area and river basins.

Laser metrology concept consolidation for NGGM

The measurement of the static and temporal variation of Earth’s gravity field yields important information on water storage, seasonal and sub-seasonal water cycles, their impact on water levels and delivers key data to Earth’s climate models. The satellite missions GOCE (ESA), GRACE (US-GER) and just recently GRACE Follow-On (US-GER) resulted in a significant improvement on our understanding of the system Earth. To further improve the measurement accuracy of the time-variable gravity field, ESA is investigating the concept of a ‘Next Generation Gravity Mission’ (NGGM), consisting of two pairs of satellites and a heterodyne laser interferometer for inter-satellite ranging. Based on the heritage of the development of the laser ranging interferometer for GRACE Follow-On and the former and ongoing studies for NGGM, two schemes for the Laser Metrology Instrument (LMI) for NGGM, namely the transponder and the retroreflector scheme have been investigated and are presented in this paper. The results include the instrument ranging performance analyses, the laser link acquisition, an instrument reliability assessment and redundancy approach as well as the Technology Readiness Level assessment of the individual instrument units.

Description of the multi-approach gravity field models from Swarm GPS data

Abstract. Although the knowledge of the gravity of the Earth has improved considerably with CHAMP, GRACE, and GOCE (see appendices for a list of abbreviations) satellite missions, the geophysical community has identified the need for the continued monitoring of the time-variable component with the purpose of estimating the hydrological and glaciological yearly cycles and long-term trends. Currently, the GRACE-FO satellites are the sole dedicated provider of these data, while previously the GRACE mission fulfilled that role for 15 years. There is a data gap spanning from July 2017 to May 2018 between the end of the GRACE mission and start the of GRACE-FO, while the Swarm satellites have collected gravimetric data with their GPS receivers since December 2013. We present high-quality gravity field models (GFMs) from Swarm data that constitute an alternative and independent source of gravimetric data, which could help alleviate the consequences of the 10-month gap between GRACE and GRACE-FO, as well as the short gaps in the existing GRACE and GRACE-FO monthly time series. The geodetic community has realized that the combination of different gravity field solutions is superior to any individual model and set up the Combination Service of Time-variable Gravity Fields (COST-G) under the umbrella of the International Gravity Field Service (IGFS), part of the International Association of Geodesy (IAG). We exploit this fact and deliver the highest-quality monthly GFMs, resulting from the combination of four different gravity field estimation approaches. All solutions are unconstrained and estimated independently from month to month. We tested the added value of including kinematic baselines (KBs) in our estimation of GFMs and conclude that there is no significant improvement. The non-gravitational accelerations measured by the accelerometer on board Swarm C were also included in our processing to determine if this would improve the quality of the GFMs, but we observed that is only the case when the amplitude of the non-gravitational accelerations is higher than during the current quiet period in solar activity. Using GRACE data for comparison, we demonstrate that the geophysical signal in the Swarm GFMs is largely restricted to spherical harmonic degrees below 12. A 750 km smoothing radius is suitable to retrieve the temporal variations in Earth's gravity field over land areas since mid-2015 with roughly 4 cm equivalent water height (EWH) agreement with respect to GRACE. Over ocean areas, we illustrate that a more intense smoothing with 3000 km radius is necessary to resolve large-scale gravity variations, which agree with GRACE roughly at the level of 1 cm EWH, while at these spatial scales the GRACE observes variations with amplitudes between 0.3 and 1 cm EWH. The agreement with GRACE and GRACE-FO over nine selected large basins under analysis is 0.91 cm, 0.76 cm yr−1, and 0.79 in terms of temporal mean, trend, and correlation coefficient, respectively. The Swarm monthly models are distributed on a quarterly basis at ESA's Earth Swarm Data Access (at https://swarm-diss.eo.esa.int/, last access: 5 June 2020, follow Level2longterm and then EGF) and at the International Centre for Global Earth Models (http://icgem.gfz-potsdam.de/series/02_COST-G/Swarm, last access: 5 June 2020), as well as identified with the DOI https://doi.org/10.5880/ICGEM.2019.006 (Encarnacao et al., 2019).